The interpretation and recognition of noisy contours, such as silhouettes, have proven to be difficult. One obstacle to the solution of these problems has been the lack of a robust representation for contours. In this paper, we present an analytical representation for contours. We introduce a smoothing criterion for the contour that optimizes the tradeoff between the complexity of the contour and proximity of the data points. We describe the computation of the contour representation, the computation of relevant properties of the contour, and the potential application of the representation and smoothing paradigm to contour interpretation and recognition.